我们先来看一下matrix completion模型的数学表达式: minXrank(X)⏟non-convex s.t. XΩ=YΩ (1) Y∈Rm×n 是一个部分观测的矩阵; Ω 是观测到的元素索引集合; X∈Rm×n 是我们希望得到的估计矩阵。 简单来说: 如果Y=[2??4]∈R2×2 是一个部分观测的矩阵,且集合 Ω={(1,1),(2,2)} ...
This optimization problem, known as matrix completion, can be made well-defined by assuming the matrix to be low rank. The resulting rank-minimization problem is NP-hard, but it has recently been shown that the rank constraint can be replaced with a nuclear norm constraint and, with high ...
low-rank matricesoptimization on manifoldsdifferential geometrynonlinear conjugate gradientsRiemannian manifoldsNewtonThe matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the...
Low-Rank Matrix Completion is an important problem with several applications in areas such as recommendation systems, sketching, and quantum tomography. The goal in matrix completion is to recover a low rank matrix, given a small number of entries of the matrix. Source: [Universal Matrix ...
The low-rank matrix completion problem [16] consists of finding the matrix with lowest rank that agrees with A on Ω: minimize X rank(X), subject to X ∈ R m×n , P Ω (X) = P Ω (A), . (1) where P Ω : R m×n →R m×n , X i,j → X i,j if (i, ...
In many cases, the data are very sparse and the matrix must be filled in before any subsequent work can be done. This optimization problem, known as matrix completion, can be made well-defined by assuming the matrix to be low rank. The resulting rank-minimization problem is NP-hard, but...
Ye. Orthogonal rank-one matrix pursuit for low rank matrix completion. SIAM J. Sci. Comput., 37(1):A488- A514, 2015.Zheng Wang, Ming-Jun Lai, Zhaosong Lu, Wei Fan, Hasan Davulcu, and Jieping Ye. Orthogonal rank-one matrix pursuit for low rank matrix completion. SIAM Journal on ...
the low-rank target matrix is written in a bi-linear form, i.e. $X = UV^\dag$; the algorithm then alternates between finding the best U and the best V. Typically, each alternating step in isolation is convex and tractable. However the overall problem becomes non-convex and...
低秩张量补全:如何从少量的观测数据中恢复出一个低秩的高维张量,这是一个非凸的、不适定的、NP难的问题。 平滑矩阵分解:如何利用张量的各个模式上的分段平滑性先验,通过对因子矩阵施加平滑约束,来提高张量补全的性能和稳定性。 块上界最小化算法:如何设计一个有效的、收敛的算法,来求解含有平滑矩阵分解的低秩张量补...
为进一步激发学校教师参与科研工作的热情,提升科研水平,促进科研辅助教学,培养高质量人才,11月2日下午,应学校科研处和工学院邀请,福州大学博士生导师王石平教授为我校师生开展题为《Differentiable Low-rank Matrix Completion》专项讲座。校长景林教授、校长助理王榕国及工学院全体教师、学生代表参加讲座,讲座由工学院院长...